Interview - Developmental Milestone Project

How to Measure Parents’ Developmental Foci: Domains and Methodologies

Chi Zhang

the University of Manchester

Sunday, the 1th of February, 2026

About me

  • PhD in Education, The University of Manchester (2021–Present);
    From belief to practice: Understanding teachers’ pedagogic choices in China’s mathematics education

  • MSc in Research Methods with Education (Distinction, 2020–2021);
    The association between mathematics teachers’ exclusivity belief and pedagogic practice

  • MA in Mathematics and Pedagogy, The Education University of Hong Kong (2019–2020)

Interview question

  1. How can one assess parents’ developmental foci in a cross-cultural context? With developmental foci, we mean the domain (e.g. linguistic, social, physical, etc.) of a child’s development that is of particular importance to parents.
  2. Think about two communities (could be Germany and Namibia, but also other contexts you have experience with) and formulate hypotheses regarding potential differences in developmental foci.

The basic IRT assumptions

What is parents’ development foci?

  • Physical and social settings of the child’s daily life;
  • Customs and practices of care; and
  • The psychology of the caretakers (Super & Harkness, 1986).

  • Cultural models of parenting and child development held by parents and others (Harkness & Super, 1996);

  • Also link to parents’ cultural belief systems/expectations/goals/focus etc.

  • “Within the constraints imposed by the wider environment, parents make choices about the best ways to take care of their children, and these choices tend to follow culturally recognizable patterns (Harkness & Super, 2020, p. 18).”

The basic assumptions of cultural models

Individualism/collectivism (e.g., Triandis, 1989); distal/proximal parenting (Keller, 2009); autonomy/relatedness (Keller et al., 2006) …

  • + : Easy to model (1|person);

  • - : Too simplified, criticisms argue autonomy and relatedness can coexist and need to coexist because they are both human needs (Keller, 2016; Oyserman et al., 2002).

Data from (Ndzenyuiy et al., 2026):

Parental Ethnotheory Questionnaire (PEQ) Item Factor Loading
It is important to rock a crying baby on the arms in order to console him/her. 0.000
Sleeping through the night should be trained as early as possible. -0.209
It is not necessary to react immediately to a crying baby. -0.321
You cannot start early enough to direct the infant’s attention towards objects and toys. -0.152
Gymnastics make a baby strong. 0.507
If a baby is fussy, he/she should be immediately picked up. 0.767
It is good for a baby to sleep alone. 0.000
When a baby cries, he/she should be narrated immediately. 0.551
Babies should be left crying for a moment in order to see whether they console themselves. -0.175
A baby should be always in close proximity with his/her mother, so that she can react immediately to his/her signals. 0.424

The basic assumptions of cultural models

For example, Kağıtçıbaşı’s (2017) four-field scheme with variations in the dimensions of agency (autonomy & heteronomy) and interpersonal distance (closeness & separateness).

  • independent self: autonomy + separateness (western middle-class, Germany)
  • interdependent self: heteronomy + closeness (rural farming community, Namibia)
  • autonomous-related self: autonomy + closeness (non-western urban community, China)
  • separated heteronomous self: heteronomy + separateness

How important is it that your child, when an adult (Liang et al., 2021)…

Item Item (stem continuation) Dimension
1 … maintains good relationships with many people? Relatedness
2 … cares about others’ feelings? Relatedness
3 … is loyal to his or her friends? Relatedness
4 … feels well connected to other people? Relatedness
5 … is well connected to the extended family (grandparents, aunts, cousins, etc.)? Relatedness
6 … tries to reach his or her goals without anyone else’s help? Autonomy
7 … tries not to depend on someone else to achieve his or her goals? Autonomy
8 … typically decides on a course of action without help from others? Autonomy
9 … makes decisions about what to do without being influenced by others’ opinions? Autonomy
10 … likes to live without many ties to others? Separateness
11 … prefers to live alone? Separateness
12 … keeps personal issues to himself or herself? Separateness
13 … does things in traditional ways? Heteronomy
14 … does the things that other people expect of him or her? Heteronomy
15 … avoids doing things that other people say are wrong? Heteronomy

Some concerns

Issues in IRT

  • Optimistic/Conservative responding style
  • Ceiling effect
  • Anchoring

Strange Results in PISA 2012

From (Kyllonen, 2015)

Example of anchors

  • Anchor in category (How often do you…. ‘half of the time’)
  • Anchor in items (items from free listing, Van de Vijver & Tanzer, 2004)
  • Anchor in context (We would like to know which of the following characteristics are important for your child when he or she has become an adult…; )
  • Anchor in modelling (Comm in fixed/random effect)

Simulation and visualisation

Simulation Settings (N=200)

  • Sample & Scale:
    • Groups: Germany (g, \(n=100\)) | Namibia (n, \(n=100\)).
    • Scale: 30 items (10 per domain), 4-point Likert, RSM (acat) logic.
  • Latent Structure (Traits):
    • Domains: L (Linguistics), S (Social), P (Professional).
    • Consistency: \(\rho = 0.6\) for same traits across domains.
    • Conflicts (\(a\) vs \(r\)): \(L = -0.2\) | \(S = -0.5\) | \(P = -0.8\) (highest tension).
  • Group n (Namibia) Specifics:
    • Trait Shift: Autonomy (a) -0.5; Relatedness (r) +0.5.
    • Response Bias: Added systematic +0.6 “optimism bias”.
    • Group g (Germany) Specifics:
    • Trait Shift: Autonomy (a) +0.5; Relatedness (r) -0.5.

Simulation via brms

ID comm Domain item resp dim_a dim_r
32 G P Pa5 1 1 0
53 G S Sa3 3 1 0
69 G S Sa2 3 1 0
88 G P Pa3 3 1 0
162 N P Pa3 2 1 0
195 N S Sr2 2 0 1 
fit <- brm(
  formula = resp ~ 1 + comm + (0 + dim_a + dim_r | ID) + (1 | item),
  data = simdata,
  family = brmsfamily("acat", "logit"), 
  prior = c(
    prior(normal(0, 3), class = "b"), 
    prior(normal(0, 1), class = "sd"),
    prior(lkj(2), class = "cor")
  ),
  backend = "cmdstanr", chains = 4, iter = 2000, warmup = 1000, cores = 4,
  file = "models/fit_rsm"
)
 Family: acat 
  Links: mu = logit; disc = identity 
Formula: resp ~ 1 + comm + (0 + dim_a + dim_r | ID) + (1 | item) 
   Data: simdata (Number of observations: 6000) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Multilevel Hyperparameters:
~ID (Number of levels: 200) 
                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(dim_a)            0.69      0.05     0.60     0.80 1.00     1426     2412
sd(dim_r)            0.68      0.05     0.58     0.79 1.00     1120     2257
cor(dim_a,dim_r)    -0.29      0.08    -0.43    -0.13 1.00      876     1712

~item (Number of levels: 30) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.72      0.10     0.55     0.93 1.01      791     1646

Regression Coefficients:
             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1]    -0.91      0.15    -1.20    -0.61 1.01      347      590
Intercept[2]     0.07      0.15    -0.22     0.35 1.01      318      453
Intercept[3]     1.11      0.15     0.81     1.39 1.01      322      425
commN            0.60      0.08     0.44     0.77 1.00     1137     1867

Further Distributional Parameters:
     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
disc     1.00      0.00     1.00     1.00   NA       NA       NA

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Visualise the base model

Figure 1: Wright map. Results from the Bayesian 1PL RSM. The leftmost panel displays item difficulty estimates across the three domains (L, S, P). The two rightmost panels highlight the community-level trait differences.

Figure 2: Community Effects. Conditional effects of Community. The left plot shows the predicted mean response. The right plot displays category-wise probabilities (1–4), demonstrating how the +0.6 optimism bias in group \(N\) shifts responses toward higher categories.

Advance model specification

fit_sep <- brm(
 formula = resp ~ 1 + comm + (0 + Domain:dim_a + Domain:dim_r | ID) + (1 | item),
  data = simdata,
  family = brmsfamily("acat", "logit"), 
  prior = c(
    prior(normal(0, 1), class = "sd"),
    prior(lkj(2), class = "cor")
  ),
  chains = 4, iter = 2000, warmup = 1000, cores = 4, backend = "cmdstanr",
  file = "models/fit_sep_dim"
)
 Family: acat 
  Links: mu = logit; disc = identity 
Formula: resp ~ 1 + comm + (0 + Domain:dim_a + Domain:dim_r | ID) + (1 | item) 
   Data: simdata (Number of observations: 6000) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Multilevel Hyperparameters:
~ID (Number of levels: 200) 
                                 Estimate Est.Error l-95% CI u-95% CI Rhat
sd(DomainL:dim_a)                    0.86      0.07     0.72     1.02 1.00
sd(DomainP:dim_a)                    0.97      0.07     0.83     1.13 1.00
sd(DomainS:dim_a)                    0.97      0.08     0.83     1.13 1.00
sd(DomainL:dim_r)                    0.91      0.08     0.76     1.07 1.00
sd(DomainP:dim_r)                    1.08      0.08     0.92     1.25 1.00
sd(DomainS:dim_r)                    0.86      0.08     0.72     1.02 1.00
cor(DomainL:dim_a,DomainP:dim_a)     0.65      0.07     0.51     0.78 1.00
cor(DomainL:dim_a,DomainS:dim_a)     0.57      0.08     0.41     0.71 1.00
cor(DomainP:dim_a,DomainS:dim_a)     0.47      0.08     0.29     0.62 1.01
cor(DomainL:dim_a,DomainL:dim_r)    -0.21      0.09    -0.39    -0.03 1.00
cor(DomainP:dim_a,DomainL:dim_r)    -0.11      0.09    -0.29     0.08 1.01
cor(DomainS:dim_a,DomainL:dim_r)     0.06      0.10    -0.13     0.24 1.00
cor(DomainL:dim_a,DomainP:dim_r)    -0.11      0.10    -0.30     0.08 1.00
cor(DomainP:dim_a,DomainP:dim_r)    -0.61      0.07    -0.73    -0.46 1.00
cor(DomainS:dim_a,DomainP:dim_r)     0.03      0.09    -0.15     0.21 1.00
cor(DomainL:dim_r,DomainP:dim_r)     0.53      0.08     0.37     0.68 1.00
cor(DomainL:dim_a,DomainS:dim_r)    -0.10      0.10    -0.29     0.10 1.00
cor(DomainP:dim_a,DomainS:dim_r)    -0.10      0.10    -0.29     0.09 1.00
cor(DomainS:dim_a,DomainS:dim_r)    -0.47      0.08    -0.62    -0.31 1.00
cor(DomainL:dim_r,DomainS:dim_r)     0.62      0.08     0.46     0.75 1.00
cor(DomainP:dim_r,DomainS:dim_r)     0.35      0.09     0.17     0.52 1.00
                                 Bulk_ESS Tail_ESS
sd(DomainL:dim_a)                    1637     2807
sd(DomainP:dim_a)                    1513     2588
sd(DomainS:dim_a)                    1841     2533
sd(DomainL:dim_r)                    1992     2607
sd(DomainP:dim_r)                    1734     2899
sd(DomainS:dim_r)                    1626     2820
cor(DomainL:dim_a,DomainP:dim_a)      785     1539
cor(DomainL:dim_a,DomainS:dim_a)      898     1864
cor(DomainP:dim_a,DomainS:dim_a)      996     1846
cor(DomainL:dim_a,DomainL:dim_r)      749     1665
cor(DomainP:dim_a,DomainL:dim_r)      789     1749
cor(DomainS:dim_a,DomainL:dim_r)     1066     2013
cor(DomainL:dim_a,DomainP:dim_r)      796     1577
cor(DomainP:dim_a,DomainP:dim_r)     1353     2254
cor(DomainS:dim_a,DomainP:dim_r)     1541     2504
cor(DomainL:dim_r,DomainP:dim_r)     1857     3098
cor(DomainL:dim_a,DomainS:dim_r)      825     1572
cor(DomainP:dim_a,DomainS:dim_r)      951     1993
cor(DomainS:dim_a,DomainS:dim_r)     1166     2379
cor(DomainL:dim_r,DomainS:dim_r)     1996     2733
cor(DomainP:dim_r,DomainS:dim_r)     2076     2828

~item (Number of levels: 30) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.83      0.12     0.63     1.11 1.00      641     1242

Regression Coefficients:
             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1]    -1.13      0.17    -1.48    -0.81 1.01      331      682
Intercept[2]     0.06      0.16    -0.28     0.38 1.01      314      708
Intercept[3]     1.35      0.17     1.00     1.66 1.01      346      724
commN            0.70      0.09     0.52     0.87 1.00      989     1790

Further Distributional Parameters:
     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
disc     1.00      0.00     1.00     1.00   NA       NA       NA

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Visualise advance model

Figure 3: Domain-specific latent correlations. Scatter plots illustrating the relationship between Autonomy (\(a\)) and Relatedness (\(r\)) across Linguistics (L), Social (S), and Professional (P) domains. Dashed lines represent the linear regressions of the recovered core conflicts, while point shapes distinguish between the German (\(G\)) and Namibian (\(N\)) communities.

Figure 4: Latent correlation matrix (\(\Phi\)) recovery. Heatmaps comparing the posterior mean estimates (left) against the target truth values (right) for the \(6 \times 6\) latent structure. The model effectively recovers the simulated correlations.

References

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Harkness, S., & Super, C. M. (2020). Why understanding culture is essential for supporting children and families. Applied Developmental Science, 25(1), 14–25. https://doi.org/10.1080/10888691.2020.1789354
Kagitcibasi, C. (2017). Family, Self, and Human Development Across Cultures: Theory and Applications. Routledge. https://doi.org/10.4324/9781315205281
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